Functional Principal Component Analysis¶
These functions are for computing functional principal component anlaysis (fPCA) on aligned data and generating random samples
fPCA Functions¶
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vert_fPCA
(fn, timet, qn; no=1)¶ Calculates vertical functional principal component analysis on aligned data
fn
array of shape (M,N) of N aligned functions with M samplestimet
vector of size M describing the sample pointsqn
array of shape (M,N) of N aligned SRSF with M samplesno
number of components to extract (default = 1)
Returns Dict containing:
q_pca
srsf principal directionsf_pca
functional principal directionslatent
latent valuescoef
coefficientsU
eigenvectors
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horiz_fPCA
(gam, timet; no=1)¶ Calculates horizontal functional principal component analysis on aligned data
gam
array of shape (M,N) of N warping functions with M samplestimet
vector of size M describing the sample pointsno
number of components to extract (default = 1)
Returns Dict containing:
gam_pca
warping principal directionspsi_pca
srsf functional principal directionslatent
latent valuesU
eigenvectorsgam_mu
mean warping functionvec1
shooting vectors
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gauss_model
(fn, timet, qn, gam; n=1, sort_samples=false)¶ Computes random samples of functions from aligned data using Gaussian model
fn
aligned functions (M,N)timet
vector (M) describing timeqn
aligned srvfs (M,N)gam
warping functions (M,N)n
number of samplessort_samples
sort samples
Returns Dict containing:
fs
random aligned functionsgams
random warping functionsft
random functions